This puzzle:

Derrick Niederman notes: The roots of this puzzle date back to the late 1970s, when I was a graduate student in mathematics. I was part of a conversation that included a question from the department chairman, a distinguished ... more

Derrick Niederman notes:

The roots of this puzzle date back to the late 1970s, when I was a graduate student in mathematics. I was part of a conversation that included a question from the department chairman, a distinguished mathematician named Michael Artin, who asked "Is it possible to create a crossword puzzle with two independent solutions?" Perhaps I should explain that "independent solutions" is classic math talk, even if being applied to another realm. Anyway, I had yet to construct a crossword puzzle (my first, a Sunday Times cryptic, came out in 1981), so he clearly wasn't looking at me, but I remembered his challenge and, years later, took it to heart.

Obviously it's not possible to create a standard American crossword with two independent solutions, but I was able to create a few pairs of British-style crosswords that did the trick. They were 13x13, with alternating keyed letters a la an American cryptic. The problem was that they were difficult to solve. There was always ambiguity about which entry should go in which puzzle, and it was very difficult to have clues that were tight and descriptive enough to remove that ambiguity. I did finally make one that was nearly perfect in that regard, but I couldn't convince Will of its worthiness and had to settle for putting it in a book.

It wasn't until a few years ago (five?) that I came up with the idea that led to MIRROR REFLECTION--namely, creating a crossword whose Across entries could be clued in balanced pairs, with the entries for radially symmetric clues being identical. I knew that the demands of the puzzle were pushing it, but it's funny what happens when you keep on plugging. (And plugging, and plugging, as in this puzzle.) Some of the balanced entries had obvious clue pairings, which was great, but I got to relish the challenge of finding clues to join words that at first didn't want to seem joined at all. And if you're curious, I can say that Will got into the game, because when I saw the finished product I noticed that one particular pair of entries (RAT/DEN, jointly clued as "Occasional basement sight") had been changed in a way that worked perfectly well.

I've had maybe 50 crosswords and cryptics published at this point, but this was the most difficult construction by far. Maybe if I did things faster that figure would be much higher than 50. After all, I've been doing this off and on for 35 years!

Jeff Chen notes: Jim said it best: 'I thought (it) was amazing. Many will hate it, I suspect, but I was impressed.' I found it to be a bold, audacious idea — EVERY across answer and its symmetrical partner uses the exact ... more

Jeff Chen notes:

Jim said it best: "I thought (it) was amazing. Many will hate it, I suspect, but I was impressed." I found it to be a bold, audacious idea — EVERY across answer and its symmetrical partner uses the exact same clue — that's memorable.

Some of the pairings were brilliant, using the type of wordplay I love: [Caterpillar product] either a PUPA (think entomology) or a PLOW (think Caterpillar, the heavy machinery manufacturer). Others were spot-on like IRONS and WOODS being a [Set of clubs in a bag], or RIDING-hood or MOTHER-hood both working equally well.

It's just amazing to think that someone would be so daring as to attempt to make EVERY SINGLE PAIR OF ACROSS ANSWERS work this way.

Now, some didn't work for me. READINGS can amount to fortunes, as in a fortune-teller reading one's palm, but SPLURGES amounting to fortunes felt grammatically tortuous. DON and NOD as anagrams for O-N-D … neither NOD nor DON would ever be clued this way normally, so that felt inelegant. Fill in the blanks with "TRIX are for KIDS" felt like it opened up just about any pairing if you located the right quote.

And the fill. Oof. As much as I loved the concept and most of the execution in the across direction — just amazing that so many of the pairs worked so well — I had a rough time swallowing DAZER. Random TEN OZ. Made-up DETAG. Odd partials OF FUN, ONCE I, ET UN. Variant TIPI. Head-scratching SSATS. Suffix -ONYM. Hits most every category that editors ask to steer clear of, and then some. Sapped my enjoyment to hit these sorts of entries throughout the puzzle.

Also, it was unfortunate not to get much bonus fill. Derrick went up to 144 words, four past Will's max of 140, which translates into very little bonus material. Just a bit of SNOWCAT, STATELINE, ANTIVIRUS.

That all said, though, the construction task is so daunting that I wouldn't have even thought to attempt it. The fact that Derrick pulled off so many great pairings is astounding, no matter what prices he had to pay to make it all work.

1. One of the blanks in the cereal slogan "___ are for ___" : TRIX5. Tinker, for one, in olden days : SHORTSTOP14. Certain blade : ROTOR19. Spread dirt, in a way : RUMOR21. Legendary Egyptian queen : NEFERTITI22. Run off : ELOPE23. Stick together : UNITE24. Liberal arts college in the Keystone State : LAFAYETTE25. Like many a lot : PAVED26. Hood lead-in : MOTHER28. Caterpillar product : PUPA29. Dud : LOSER31. Historical period : ERA32. One of Frank's wives : AVA33. Member of the cat family : FELINE35. Father, familiarly : REV36. Japanese auto make : NISSAN38. Court concern : NET39. Big Australian export : TIN40. One of five on a starfish : RAY42. Set of clubs in a bag : IRONS44. These could amount to fortunes : READINGS48. Dead follower : SEA50. Where to find grooms : ALTARS53. Vingt-___ (multiple de trois) : SEPT54. This does not fly : TWA56. Anagram of the letters O-N-D : NOD58. State with part of I-81: Abbr. : TENN60. What you might call a dog : SPOT62. Instrument for an angel : HARP63. Caspar, Melchior and Balthazar, e.g. : TRIO65. Something you can do with flies : SHOO66. First name of an Oscar-nominated actress of 1957 : LANA67. Time in ads : DATE68. Square ___ : INCH69. Animal in an Aesop fable : OWL70. White House sight : ROSEGARDEN72. White House sight : OVALOFFICE75. Animal in an Aesop fable : ASS76. Square ___ : DEAL77. Time in ads : NITE78. First name of an Oscar-nominated actress of 1957 : ELSA79. Something you can do with flies : SHAG81. Caspar, Melchior and Balthazar, e.g. : MAGI82. Instrument for an angel : LYRE83. What you might call a dog : MUTT84. State with part of I-81: Abbr. : PENN85. Anagram of the letters O-N-D : DON86. This does not fly : EMU87. Vingt-___ (multiple de trois) : ETUN89. Where to find grooms : STABLE92. Dead follower : EYE94. These could amount to fortunes : SPLURGES98. Set of clubs in a bag : WOODS100. One of five on a starfish : ARM102. Big Australian export : RUM103. Court concern : LAW105. Japanese auto make : DATSUN108. Father, familiarly : POP110. Member of the cat family : OCELOT113. One of Frank's wives : MIA114. Historical period : AGE115. Dud : LEMON117. Caterpillar product : PLOW118. Hood lead-in : RIDING120. Like many a lot : ZONED122. Liberal arts college in the Keystone State : DICKINSON125. Stick together : PASTE126. Run off : ERODE127. Legendary Egyptian queen : CLEOPATRA128. Spread dirt, in a way : INTER129. Certain blade : RAZOR130. Tinker, for one, in olden days : ITINERANT131. One of the blanks in the cereal slogan "___ are for ___" : KIDS